Dynamical Models in Semiotics/Semantics

Lecture One: From Discrete Signs To Dynamic Semantic
Continuum

We shall begin by arguing against the tendency (as in structural
linguistics) to study meaning from the point of view of discrete
sign units, and then identify approaches where a continuous plane
of content is characterized by spatial and actantial relations
between entities. Subsequently, we shall go on to examine two
theories that view sentence-meaning in terms of a) holistic
structures and b) constraints imposed on the structure of language
by the essentially dynamic and constantly transforming nature of
the world. These two approaches are: 1. Catastrophe theoretic
semantics proposed by mathematician Rene Thom based on the concept
of morphogenesis, and 2. Karaka theory of the Sanskrit
grammarians, particularly the version elaborated by the 7th century
philosopher of language, Bhartrhari. By highlighting these theories
we are suggesting that the relation between language and 'reality'
can be seen as a matter of reflection/revelation of the infinite
dynamism of the world by means of a finite variety of basic
sentence structures. We shall also emphasize the importance of the
gestalt conceptions present in the two theories.

Discrete Signs?

We know that in the structural linguistics founded by Ferdinand de
Saussure, the linguistic sign is understood as an inseparable
bipartite entity constituted of a signifier and a signified.
Saussure saw the langue (language system) as made up of
discrete signifying units or signs defined in terms of their
relations and mutual differences, and which enter into acceptable
combinations in language use (parole). While the sound-form
and thought, mediated by language, are continuous and 'nebulous' in
nature, language itself is constituted of discrete, discontinuous
signs. Saussure excludes from the realm of language the undivided
streams of both thought and of sound-form. Important to this
conception of language is the simultaneous and parallel
discretization of both signifiers and signifieds, and the modes of
reconstitution of the formal and semantic unity by means of
syntagmatic combinations. Syntagmatic and associative/paradigmatic
relations "are two forms of our mental activity, both (of which)
are indispensable to the life of our languages" (Course, 123).

We notice that Saussure is upholding the widely held belief that
language is a rule based system of discrete symbolic units and
their combinatorial behaviour. (This idea has been further
reinforced by N. Chomsky who while centring his linguistics on
syntax stresses on the computational and arbitrary character of
human language.) Thus, even while insisting on the complete
autonomy of language, Saussure readily accepts the view that
"language, in a manner of speaking, is a type of algebra consisting
solely of complex terms" (ibid., 122).

As regards the nature of the combinations of signs, Saussure
appears to be far less committed. The temporal order of the spoken
language imposes on it a character of linearity, and this
necessitates the sign units to be "linked together." Syntagms are
"combinations supported by linearity." (ibid., 123) Here, indeed
there is a paradox that Saussure himself reveals to us: while
syntagms are combinatorial constructs defined by reciprocal
occurrence, "the sentence is the ideal type of syntagm." (ibid.,
124) However, the latter belongs to speaking (i.e., parole) and not
to the language system. Thus, at the level of combinatorics,
Saussure perceives a continuum of more or less constructional
rigidity, the least rigid syntagmatic unit being the sentence,
which indeed is not a unit of the language system, but of speaking.
Saussure's solution is as follows:

" ...in the syntagm there is no clear-cut
boundary between the language fact, which is sign of the collective
usage, and the fact that belongs to speaking and depends on
individual freedom. In a number of instances it is hard to class a
combination of units because both forces have combined in producing
it, and have combined in indeterminable proportions." (ibid.,
124)

Just as he has an excellent sense of the sign as the basic,
independent unit of language, Saussure is also conscious of the
coexistence of signs in a totality: "Language is a system of
interdependent terms in which the value of each term results solely
from the simultaneous presence of the others ..." (ibid., 114). A
language-totality is thus the sum of all its sign-units, and their
relations, both syntagmatic and paradigmatic.

Perhaps, by overstating the autonomy of language structure,
Saussure remains insensitive to the specific structuring of the
sentence, both at the syntactic and semantic levels. While
concentrating on a description of the individual signs as well as
on the language-totality, Saussure seems to have paid very little
attention to the syntactico-semantic constitution of the sentence.
Indeed, true to the positivist tradition that he had inherited from
the 'neo-grammarians', Saussure was seeking to constitute the
'objectivity' of language. Thus, the language system had to be 'out
there', and in the ultimate analysis, in the human mind, organized
in terms of the syntagmatic (in praesentia) and associative
(in absentia) relations.

What is missing in the Saussurean perspective, from our point of
view, is an 'ecological' perspective on language. Language is not
an entirely objective system, determinable either externally or
internally. It is made to the measure of man, enabling him
to situate himself in the world, and communicate with other human
beings that forms part of his environment. From this perspective,
the linguistic structure is ideally capable of representing
the dynamic nature of the world -- physical and social --, and
perception is the biologically-given cognitive means to mediate
between the dynamic structure of the world and the linguistic
structure. This isomorphism between the language and the world,
mediated by holistic perceptual structures, can be represented only
by the sentence, and not by isolated signs, be it words, morphemes,
or phonemes.

The grammatical notion of sentence, we know, has been central for
linguistics of the classical periods, both in the European and the
Indian traditions. In Europe -- for those who insisted on its
centrality -- the sentence was seen as the minimal unit of
expression of a complete thought, containing a subject and a
predicate component. As per this view, prevalent from, Aristotle to
Port-Royal, only the sentence can have a truth-value. After listing
his famous ten Categories of expression, Aristotle says:

"Not one of these terms in itself will
involve any positive statement. Affirmations and also denials, can
only arise when such terms are combined or united together. Each
positive or negative statement must either be true or false -- that
at least, is allowed on all hands -- but an uncombined word or
expression (for instance, 'man', 'white', 'runs' or
'conquers') can neither be true nor be false." (quoted in Harris
and Taylor, 1989: 26-27).

In India too, there were profound and meaningful debates between
scholars who held that the sentence conveyed undivided meaning
(akhanda-pakshavada) and those who held that sentence meaning
is a result of the combinatorics of word-meanings (padavada).
Bhartrhari was a firm adherent of the former position. Here
too, the infra-sentential units, such as the subject and the
predicate were considered incomplete. Alone, they leave a blank
which needs to be filled by a corresponding element to form a
complete and independent unit, the sentence. The traditional
grammatical term for this cognitive-grammatical lack and its
potential satisfaction, was Akanksha or expectancy. It is
expressive of the polarity between the major linguistic categories
such as the noun and the verb, and their mutual formal attraction.

Though the understanding of language structure in terms of
syntagmatic and paradigmatic relations is extremely useful, it is
still important to perceive the hierarchical organization of the
language units, which the tree-structures of Chomskyan generative
grammar or the 'stemmas' of Lucien Tesniere attempt to capture.
Language is a system where the multiple levels of organization of
form and meaning are masked by a surface linearity. Sentence is not
only the highest level of this hierarchy, but also, in relation to
thought, the bounding structural unit. (Beyond the sentence, of
course, there is the textual level which may also have its
hierarchical organization, for instance, of the narrative units.)
Etymologically speaking, a 'sentence' expresses what is felt or
thought ('sentir'). It is worth recalling that in the Aristotelian
conception, language is a mode of representing or imitating reality
(mimesis), involving the use of a subject-predicate structure. It
appears that in his linguistic definitions, Aristotle had sought to
distinguish between the perceptual-cognitive dimension ( world-mind
relation) relevant for language and the actual
conventional-symbolic dimension (mind-word relation). However, the
symbolic dimension is both complicated and reinforced by
Aristotelian conception of metaphor which he defined as a process
of semantic transfer, capable of introducing , possibly and not
entirely predictably, ever-new linguistic conventions. Other modes
of representation such as painting, music or drama do not have this
sort of a mimetic structure, and hence can not be evaluated in
relation to the truth or the falsity of the representation.

Hjelmslev: The form of content and the spatial conception of
cases

Luis Hjelmslev recognized that in relation to text, meanings are
not attached to the signifiers in a one-to-one manner within
identifiable sign-units. He undermined the idea that the signified
and the signifier are bound together in a complementary manner
within discrete sign units. Instead he proposed a linguistic
description that

"must analyze content and form
separately, with each of the two analyses yielding a restricted
number of entities, which are not necessarily susceptible of
one-to-one matching with entities in the opposite
plane."(Hjelmslev, 1961 edn.:45)

In the place of the Saussurean bipartite division of the sign,
Hjelmslev introduced a quadripartite notion of the sign. Clarifying
the Saussurean conception of language a little further, Hjelmslev
insisted that the elements of the thought and the sound realms do
not enter into direct and unmediated unity to form the sign, but
that they have to be mediated by the form of particular languages.
In addition to Saussure's linguistic a prioris of thought
and sound (which in his new systematization becomes
content-substance and expression-substance respectively), Hjelmslev
introduces the notions of content-form and expression-form. Both
the content-substance and the content-form do not exist anterior to
the specific semiotic functions ('purport') that a language is put
to use by its speakers. As per this view, the content-substance
(i.e., the unit of thought) is formed by the action of the
content-form upon the purport. Hjelmslev suggests that the domain
of colours can be taken as an example of purport, "which,
abstracted from (...) languages, is an unanalyzed, amorphous
continuum, on which boundaries are laid by the formative action of
the languages."

It is in relation to such a context that Hjelmslev's penetrating
analysis of the category of case must be seen. A significant part
of his famous 'La Categorie des Cas' (1935) is devoted to a
detailed historical account of the different approaches to a theory
of the grammatical case. Since there is no language where the
case-system does not have a significant function, Hjelmslev
believes that it is necessary for any grammatical study to begin
with an analysis of the case category.

In his effort to determine the 'constant system' and the
'structural principle' associated with the diverse manifestations
of it, Hjlemslev has undertaken a detailed historical analysis of
the views for and against the localist conception of the
case category. The idea was first proposed in the middle ages by
the Byzantine grammarians, Maxime Planude and Theodore of Gaza. In
recent times, it has been revived by John Anderson (1971) and
Charles Fillmore (1977). Th. Gaza interpreted case-relations in
terms of spatial movements, e. g., the accusative case as denoting
the grammatical subject as directing its activity towards the
object, and the genitive as denoting the subject as receiving or
absorbing an object.

In the modern period, innovative proposals were made for treating
the cases and prepositions as belonging to a common semantic
category. Bernhardi (1805), for instance, conceived of the
case-morpheme as a 'condensed preposition'. Another important idea
was that of G. M. Roth (1815) who sought to treat case as a
category signifying 'relation', explicitly founded on the Kantian
category of 'relation'. This view that the case category signified
'relation' seems to have been widely held during most of the 19th
century, with or without Kantian underpinnings. Attempts were made
during this period to link the linguistic categories with basic
epistemological categories. It was felt that concepts of the deep
linguistic level were of the same type as the
logical/epistemological concepts.

In about the same period, Franz Bopp introducing his own version of
localism saw a connection between 'primitive expressions of spatial
order' and the expressions of time and causality, which he
considered as attributes of more complex thought. Bopp's student,
Wullner, directly transposing some of the basic tenets of Kantian
philosophy on linguistic analysis, set up three principles. These
are:

subjectivity, as per which the
phenomena denoted by the linguistic sign was not of objective, but
of subjective order; the speaking subject chooses a particular
grammatical form not according to any objective requirements
imposed by the real state of things, , but according to the idea or
conception with which he regards the objective fact;

fundamental signification which can be identified at a certain
degree of abstraction, and which permits the deduction of all the
concrete uses of a linguistic form; and

of empirical method in language study.

On the basis of his long historical survey of positions for and
against localism in linguistics Hjelmslev goes on to make a
structural delimitation of the case category. Since there are
cases or case-like elements in all languages, it is possible to
identify this category as a linguistic subsystem having a definite
range of significations, or rather, being based on a 'fundamental
signification' that manifests with minor variations in all
languages.

Hjelmslev follows a Kantian epistemology rather closely, and adapts
it for the purposes of his own structural linguistics. In the place
of the Kantian notion of 'function', Hjelmslev introduces the
notion of 'expressed value' (valeur exprimee). A grammatical
category is thus to be defined by its value, and simply as an
expression."A linguistic form is an expressed value. The relations
that we are concerned with are thus in all languages, expressed
values."

Following Wullner principles and his own Kantian elaboration of
them, Hjelmslev goes on to claim that "grammar is the theory of
fundamental significations or values, and of systems constituted by
them ..." In fact, the actual definition of the category of case
that he arrives at is a complex consisting of:

the concrete significations of
its various manifestations (directionality, dependence-independence of objects, etc.);

a notion abstracted from these diverse significations, i.e.,
the 'fundamental signification', and

the spatial conception.

The system of fundamental signification for the case at this stage
appears to consist of 3 dimensions:

Direction ("eloignement"
[distancing] -- "rapprochement" [nearing);

A double conception of direction, namely
dependence-independence;

Subjectivity -- Objectivity.

In order to deal with the theoretical difficulties regarding the
first of the above dimensions, Hjelmslev says that certain specific
linguistic attributes must be taken into account. He insists that
language cannot be reduced to pure and simple principles of logic;
the logico-mathematical type of opposition (e. g., positive and
negative) is not the only type of opposition to be found in
language. For instance, on the direction dimension what we see is
not a relationship of opposition, i.e. the presence of one feature
implying the absence of the opposite. Instead of a logical system
based on a law of opposition or of non-contradiction, languages,
Hjelmslev suggests, are guided by a prelogical system with
its own 'law of participation'. The opposition is not between one
language having a feature A, and another language having a feature
non-A, but it is of having the features A and non-A in the same
language. A pre-logical (non-oppositional, participational)
character of language is exemplified by the fact that "the normal
system of Latin as it is obtained in the traditional grammar is
organized on the basis of the ablative, whereas the system of Greek
is organized on the basis of the accusative." Between the ablative,
with its feature of [- rapprochement] and the accusative with its
feature of [+ rapprochement], on the direction dimension, there is
no opposition, but there are only different orientations
while the case with the supposedly opposite feature is present in
one and the same language.

Hjelmslev observes that it is not surprising to find a prelogical
system in natural language, especially in the light of Lucien
Levy-Bruhl's demonstration of a 'pre-logical mentality' (originally
attributed to a 'primitive mentality') in all languages.
According to Levy-Bruhl, the prelogical mentality is characterized
by a community's collective representations involving the 'law of
participation'. It is 'most often indifferent to contradiction'
(Levy-Bruhl, 1922: 88). Further, the prelogical mentality is
'essentially synthetic'. It is not a synthesis involving a prior
analysis into concepts, but where "the connecting links of
representations are given with the representations themselves."

An important feature of the prelogical mentality is the strong
sense of space and time. Devoid of a 'logical' unity of the object,
for the prelogical mind, "the same object, in different
circumstances may have different meanings." (ibid., 117) Levy-Bruhl
notes that the central feature of the prelogical knowledge is that
of 'preformed connections':

" ...if connections are the chief
consideration, we pronounce it as prelogical. By prelogical we do
not mean to assert that such a mentality constitutes an ante-cedent
stage, in point of time, to the birth of logical thought. Have
there ever existed groups of human beings, or pre-human beings
whose collective representations have not been subject to the laws
of logic?" (ibid. 78)

The prelogical is neither anti-logical nor alogical. The 'logical'
which is sensitive to the law of contradiction and the
'prelogical' which obeys law of participation always coexist.
Hjelmslev echoes Levy-Bruhl's view that the prelogical mentality is
far from extinct, and that it coexists with the 'pensee logique' in
modern societies, "more or less independent, more or less subdued,
but ineradicable" (Levy-Bruhl, 1936: 243). This coexistence of two
different mentalities is an inevitable fact, for:

["...logical thought can never be the universal inheritor of
prelogical mentality. There will always be collective
representations which express a participation intensely felt and
lived, whose logical contradiction nor its physical impossibility
can never be demonstrated."]
(ibid., 241)

However, instead of wanting to maintain the relative autonomy of
the prelogical, Hjelmslev's curious strategy towards the end of the
theoretical part of his 'La categorie' is to forge what he calls a
'sublogical system' which will bring under a common principle both
the prelogical system and the system of formal logic. This, in his
view, is the best structural solution.

The sublogical system that lies "at the base of both the logical
system and the prelogical system" consists of representing the
principal points of the relevant conceptual zone. The procedure is
to identify the fundamental signification in terms of positive and
negative values, and zero when necessary, without resorting to all
the possible nuances of formal logic, and without admitting all
possible extensional configurations. (Hjelmslev, 1935: 127)

The conceptual zone concerning the system of case and prepositions
is that of the relations between two objects on a spatial plane.
The 'dimensions' of these relations are:

1. Direction:

Rapprochement (nearing) and

eloignement (distancing)

------>~~I

I~~----->

2. Coherence - Non-coherence:
These are relations with or without contact; the former is further
divided into Interiority and Exteriority.

3. Subjectivity - Objectivity:
Here there are two axes; the vertical axis represents objectivity
(the relations involving 'above' and 'below' or 'under' are
independent of the speaking subject's perspective), and the
horizontal axis represents subjectivity ('before' and 'after' are
oriented to the speaker's perspective).

The Actantial Paradigm

Alongside the unit-to-unit correspondence between language and the
world, which has been in vogue since the Socratic Greek tradition,
we can also observe interest in a figure-like adequation of
language to reality. Thus, in addition to the logical/
propositional value of the sentence implicit in the former,
philosophers and linguists have considered sentence as a mode of
reflecting events in the world in a somewhat pictorial manner.
Lucien Tesniere, for instance, has proposed such a view in his
Elements de syntaxe structurale (1959). His purported goal
was to found a science of the sentence, or Syntax. The so-called
'dependency' grammar of Tesniere is based on an implicit notion of
'action' which was also central to the ancient Indian grammarians.
For Tesniere, the meaningfulness of a sentence was due the central
organizing role of the predicate verb which represented an action,
and functioned as the highest syntactic node of the sentence. The
verb is the complete and the independent term of a sentence.
Dependent on the verb are the 'actants' which are the participants
in the action. (This dependency relation is diagrammatically
represented by means of a tree-structure or 'stemma'). Tesniere
viewed the sentence as representing a 'little drama' (un petit
drame) wherein the predicate represents an action (in the
theatrical sense), or even a process, and the dependents of the
predicate are the principal elements in the action. Since Tesniere
distanced himself from a logical conception of grammar, he also
eschewed the Subject-Verb-Object-Indirect-Object type of
propositional analysis. He opted for a rather theatrical conception
where the nominal elements are initially non-heterogeneous actants
participating in a process, but appearing in their functionally
specialized roles as subject, object and indirect object in the
context of the sentence- structure. Tesniere defines actants as
"beings or things which in some capacity and in whatsoever manner,
even in the capacity of mere onlookers and in the most passive
manner participates in a process." (Tesniere, 1959/1988 :102).
According to him the interrelationship among the actants belonged
to the structural order (distinct from the linear sentence order)
and hence to a 'dynamic' syntax.

While the actants are one type of dependents of the predicate (they
designate characters in a anthropomorphic sense), the other type
called the circumstants designate the spatio-temporal situation or
the manner. According to Tesniere there can be a maximum of only
three actants in a sentence while the circumstants may be several.
The following example may suffice as an illustration:

Sentence:Mohan bought an electronic camera for his son yesterday.

Stemmatic representation:

Here, A1 (= Mohan) is the First actant or the Subject, A2 (=
Camera) is the Second actant or the Object of the transitive verb
or the agent of the passive verb, A3 (= son) is the Third actant,
or the Beneficiary, and (C = yesterday) is the circumstant.

Tesniere's dependency grammar is a kind of case-grammar describing
the semantic roles of sentence constituents. We may note that he
had also introduced the notion of "valency" to denote the number of
actants carried by a verb. Thus the valency could be zero ('rain'),
one ('cry'), two ('hit') or three (`give'). The notion of valency
helps us to have clearer idea of the relationship between the
actantial dynamics and its perceptual organization one hand,
and the case-structures on the on the other. The action associated
with a zero-valent verb, 'rain' pervades the whole of the
perceptual frame, and hence linguistically manifests itself with no
grammatical subject, or a so-called 'dummy subject' as in many
languages, like English (it) and French (il), or even
an Absolute subject as in Arabic. Uni-, bi-, and tri- valent verbs
represent actions with increasing complexity, and hence yield
correspondingly different case-structures, such as the nominative,
the accusative, and the dative, etc.

Despite their apparent similarity, Tesniere's stemma is different
in content from Chomsky's tree-diagram. While in the latter, the
connections between the nodes have no theoretical value, in the
former these connections are perceived in an organic way, that is,
as the connections between the participants in an action. The
stemmas are the diagrammatic representation of a holistic image of
the meaning of the sentence meaning conceived as action. They are
suggestive of the sentence-meaning as some sort of dynamical
gestalts.

We notice that Tesniere is trying to describe a semantic continuum
underlying the surface sentence structure. His starting definition
is: "A sentence is an organized ensemble whose elements are the
words." Further: "Every word which forms part of a sentence ceases
itself to be isolated as in a dictionary. Between it and its
neighbours, the mind perceives connections whose ensemble forms the
framework of the sentence ...These connections are indicated by
nothing. The sentence can be comprehended only when the mind
perceives these connections" (Tesniere, 1959: 11). For example in
the sentence, "Alfred speaks, "there are three elements: 1. Alfred,
2. speak, and 3. the connection which unites the two first
elements, and without which they would not form a sentence. Not to
account for the connections "is to ignore the essential, which is
the syntactic link." "The connection is indispensable for the
expression of thought. Without connection, we will not be able to
express any thought, and we will only be uttering a succession of
images and indices, isolated from each other, and without any link
between them." (ibid., 12) Thus it is the connection that gives the
sentence its organic and living character, and is its vital
principle. Tesniere sought to relate his organicist and vitalist
ideas on language to Humboldt's description of speech activity as
'energeia' in opposition to the 'ergon' or the static
aspect of language, or langue. On the importance of connections,
Jean Petitot remarks: " ...a sentence is above all a system of
connections which being 'incorporeal' (non sensible) can only be
grasped by the mind. These structural connections, oriented and
hierarchised, are not of logical essence, but constitute an
'organic and vital' principle of organization ..." (Petitot,
1985:45).

In Tesniere's idea of the sentence, its linear order represents the
actantial dynamics in the world by means of the verb, the actants
and the circumstants. But its structural and dynamic order, though
not linguistically manifested, is perceived by the mind. The linear
sentential order transposes itself upon the dynamic and structural
order in diverse ways depending upon the specific typology of the
language considered.

The actantial perspective and the notion of structural connections
are part of Tesniere's theatrical perspective on the sentence
structure, developed at least in part to facilitate
grammatical pedagogy. Indeed, he whole-heartedly supported an
organicist and holist conception of the sentence. The advantage of
such a position is that it permits us to think of a structural
space where the actants are related to each other via the activity
referred to by the verb. Among other scholars who have maintained
similar views is the Russian linguist, S. Katznelson who, while
noting the fragmentary nature of words as against the holistic
character of sentence observes that it is the "grammatical elements
...(that) re-establish the living links which full words tend to
lose when they are withdrawn from the images of coherent events."
(Katznelson, 1975: 102)

Tesniere's fundamental ideas of actant and valency as well as his
organicist perspective has much influenced the semiotic/semantic
thinking of Rene Thom known for his Catastrophe Theory. The central
role assumed for the verb in virtue of its signifying an
action/interaction, and of its assigning actantial roles is also a
common factor between the systems of ideas of Tesniere and Thom.